 If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. In the two polygons ABCDE and A'B'C'D'E', let the triangles AEB, EEC, CED be similar, respectively, to the triangles A'E'B',...  Elements of Geometry and Trigonometry: With Notes - Page 73by Adrien Marie Legendre - 1828 - 316 pagesFull view - About this book
 | John Charles Stone, James Franklin Millis - Geometry - 1916 - 306 pages
...the corresponding vertices E and Q, instead of the diagonals from A and M. 138. Theorem. — If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. L23° 'BMN Hypothesis. Polygons ABCD ••• and MNOP •••... | |
 | William Betz, Harrison Emmett Webb - Geometry, Solid - 1916 - 214 pages
...proportional between the whole hypotenuse and the adjacent segment. 412. If two polygons are similar, they are composed of the same number of triangles, similar each to each and similarly placed. 415. The perimeters of two similar polygons are to each other as any two homologous sides.... | |
 | Webster Wells, Walter Wilson Hart - Geometry - 1916 - 504 pages
...B AF + BD~ + CE = AE + BF2 + CD . " D PROPOSITION XV. THEOREM 293. Two polygons are similar if they are composed of the same number of triangles, similar each to each, and similarly placed. Hypothesis. AA EB ~ A A'E'B' ; A EBD ~ A .E'B'D' ; ABCD-AB'C'D'. The triangles are similarly... | |
 | Herbert Ellsworth Slaught - 1918 - 344 pages
...perimeter of the larger. SIMILAR FIGURES TRIANGLES FORMING SIMILAR POLYGONS 362. THEOREM XV. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, then the polygons are similar. B' Given polygons P and P, composed of AI, II, III, and I',... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1918 - 360 pages
...inches, find the perimeter of the larger. TRIANGLES FORMING SIMILAR POLYGONS 362. THEOREM XV. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, then the polygons are similar. B — — n B' Given polygons P and P, composed of AI, II, III,... | |
 | Encyclopedias and dictionaries - 1920 - 934 pages
...similar. Two triangles which have their sides parallel or perpendicular, each to each, are similar. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. In solid geometry, similar polyhedrons are those whose corresponding... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...similar. PROPOSITION XXV. THEOREM (303) (303) (Ax. 1.) (309) Q. E D. 314. Two polygons are similar if they are composed of the same number of triangles, similar each to each, and similarly placed. Given in the polygons ABCDE and A'B'C'D'E', AABE~ AA'B'E', ABCE ~ AB'C'E', A CDE ~ A C'D'E',... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry - 1918 - 460 pages
...AB AC BC DC AD DB (1) 13 12 (2) 12 i (3) 16 4 (4) 20 12 (5) 30 50 SIMILAR POLYGONS 441. Two polygons composed of the same number of triangles, similar each to each and similarly placed, are similar polygons. 442. Problem. Construct a polygon similar to a given polygon having given... | |
 | Encyclopedias and dictionaries - 1920 - 934 pages
...similar. Two triangles which have their sides parallel or perpendicular, each to each, are similar. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. In solid geometry, similar polyhedrons are those whose corresponding... | |
 | Education - 1898 - 634 pages
...a given point a parallel to a given straight line. 9. Show that two polygons are similar when they Are composed of the same number of triangles, similar each to each and similarly placed. 10. Show that two triangles having an angle of one equal to an angle of the other, are to each... | |
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